Sensitivity enhancement of grating interferometer based two-dimensional sensor arrays using two-wavelength readout Onur Ferhanoglu and Hakan Urey* Department of Electrical Engineering, Optical Microsystems Laboratory, Koç University, Sarıyer, Istanbul 34450, Turkey *Corresponding author:
[email protected] Received 8 December 2010; revised 5 May 2011; accepted 10 May 2011; posted 13 May 2011 (Doc. ID 139104); published 29 June 2011
Diffraction gratings integrated with microelectromechanical systems (MEMS) sensors offer displacement measurements with subnanometer sensitivity. However, the sensitivity of the interferometric readout may drop significantly based on the gap between the grating and the reference surface. A twowavelength (2 − λ) readout method was previously tested using a single MEMS sensor for illustrating increased displacement measurement capability. This work demonstrates sensitivity enhancement on a sensor array with large scale parallelization (∼20; 000 sensors). The statistical representation, which is developed to model sensitivity enhancement within a grating based sensor array, is supported by experimental results using a thermal sensor array. In the experiments, two lasers at different wavelengths (633 and 650 nm) illuminate the thermal sensor array from the backside, time-sequentially. The diffracted first order light from the array is imaged onto a single CCD camera. The target scene is reconstructed by observing the change in the first diffracted order diffraction intensity for both wavelengths. Merging of the data from two measurements with two lasers was performed by taking the larger of the two CCD measurements with respect to the reference image for each sensor. ∼30% increase in the average sensitivity was demonstrated for a 160 × 120 pixel IR sensor array. Proposed architecture is also applicable to a variety of sensing applications, such as parallel biosensing and atomic force microscopy, for improved displacement measurements and enhanced sensitivity. © 2011 Optical Society of America OCIS codes: 050.1950, 120.3180, 120.2830.
1. Introduction
Diffracting gratings embedded under microelectromechanical systems (MEMS) sensors provide subnanometer displacement measurements for various sensing and imaging applications such as atomic force microscopy [1,2], MEMS based Fourier transform IR spectrometers [3,4], biomolecular force spectroscopy sensors [5], resonant mass biosensors [6,7] and thermal imaging [8,9]. A displacement resolution as low as 3 fm⋅Hz−1=2 was demonstrated by state of the art membrane based force measurement sensors incorporating diffraction grating readout [5]. 0003-6935/11/193289-07$15.00/0 © 2011 Optical Society of America
Despite its ultrahigh displacement sensitivity, interferometer based readouts are limited to an unambiguous range of λ=4 for a single, narrowband illumination source. Furthermore, the sensitivity may be degraded significantly based on the sensor position. For active sensors where the gap between the sensor and diffraction grating can be controlled, the gap is typically tuned to the maximum sensitivity given by the highest slope of the intensity versus gap curve. When the sensor is tuned for maximum sensitivity, a displacement of λ=8 brings the sensor sensitivity essentially to zero. Recently, an integrated dual-grating method has been proposed [10], where two gratings with λ=8 height difference that results in a 90 ° phase shift to the incoming light are placed underneath a membrane sensor. The quadrature 1 July 2011 / Vol. 50, No. 19 / APPLIED OPTICS
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signal acquired using phase-shifted double grating, results in constant sensitivity that is equal to the sensitivity achieved at the maximum sensitivity point using a single grating. Another method for achieving constant, high sensitivity and extended range readout was demonstrated through active control of a micromachined scanning grating interferometer. The sensor was electrostatically controlled using a modified recurrent calibration based path stabilization algorithm [11] to remain at the maximum sensitivity point. The aforementioned methods are beneficial for either a dual-grating based sensor that can afford a significant amount of space for its reference reflector or an active sensor whose gap can be controlled. Integrating multiple sources into the readout is a robust solution especially for passive sensor arrays, which enhances both the range and the sensitivity of the displacement measurement. 2 − λ interferometry was first implemented starting in the early 1970s [12,13]. The 2 − λ readout for diffraction grating interferometers as a method for maintaining the sensitivity for a large range of displacements were previously demonstrated [14,15]. The most important advantages of the 2 − λ readout of grating based sensor arrays can be summarized below.
2. Two-Wavelength Grating Interferometry
Figure 1(a) illustrates a diffracting grating based sensor. The sensor is fabricated on a transparent substrate and consists of an embedded fixed grating placed underneath the sensor and a reflector that is placed on top of the sensor. The illumination is performed from the bottom side. Fixed grating and the reflector form an interferometer where the movement of the sensor modulates the optical path difference and the resultant diffraction order intensities. Well known formulas for the zeroth and odd diffracted order light can be expressed as 2πg 2 I 0 α cos ; λ
ð1Þ
1. No change in the sensor structure: an additional laser source can be placed in the optical train without difficulty. 2. No electrical interconnects to the sensor: the 2 − λ readout method requires no active tuning of the sensor that makes it more suitable for passive sensor applications such as the thermal imaging sensor arrays [8,9]. 3. Extended range: using the 2 − λ readout method, the unambiguous displacement detection range is increased from quarter wavelength λ1 =4 up to ðλ1 ⋅λ2 Þ=4jλ1 − λ2 j, where λ1 and λ2 are the readout wavelengths. For λ1 ¼ 650 nm and λ2 ¼ 633 nm, this implies an enhancement of the range from 160 nm up to 6 μm. This advantage was previously demonstrated using a dynamic diffraction grating based Fourier transform spectrometer [14]. 4. Enhanced sensitivity: the 2 − λ readout method provides displacement measurement up to the ∼1 μm range with >60% maximum sensitivity and the ∼1:7 μm range with >50% maximum sensitivity using the above wavelengths. Corresponding ranges for the single wavelength readout case (λ ¼ 633 nm) are only 95 and 105 nm, respectively. This paper presents the basic 2 − λ sensor readout principle, defines the sensitivity of the 2 − λ readout method, and extends the analytical modeling to a two-dimensional (2D) array of sensors considering the statistical variations of various nonuniformities inherent in the sensor. Experimental demonstration of the sensitivity improvement is performed on a 2D grating based thermal imaging sensor array with 20, 000 sensors. 3290
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Fig. 1. (Color online) (a) Diffraction grating based MEMS sensor on a transparent substrate that is illuminated with two lasers with wavelengths λ1 and λ2 (b) Proposed method using two-wavelength illumination where the sensor array, with gap variation, is illuminated by two sources, one at a time. The diffracted first order light is imaged onto an array of photodetectors, i.e., a CCD camera. (c) Details of the thermal imaging experiment where the blackbody radiation emitted from an IR heater that is covered with an aperture is imaged onto the thermomechanical sensor array.
2πg 2 I odd α sin ; λ
ð2Þ
where g is the gap between the sensor and the fixed grating and λ is the wavelength of illumination. Since the intensity variation of all orders is periodic with respect to g, the range of the interferometric readout is bounded to an unambiguous range of λ=4. Furthermore, the sensitivity, defined as the rate of change of intensity with a gap, can severely diminish near the peaks and the dips of the sinusoidal intensity curve. Note that the highest absolute sensitivity is achieved where g ¼ λ=8 þ k⋅λ=4 and the lowest (zero) sensitivity is achieved where g ¼ k⋅λ=4 for any positive integer k. Figure 1(b) illustrates a setup suitable for the sensor array readout by monitoring first diffraction orders with a single CCD camera. The 2D sensor array is uniformly illuminated in one shot, by expanding and truncating two lasers with wavelengths λ1 and λ2 time-sequentially. Alternatively, the readout can be accomplished by monitoring each source with a different camera simultaneously, in the expense of higher cost and larger space. The normalized sensitivity for either one of the wavelengths and the combined sensitivity of the 2 − λ readout system for the first diffracted order can be defined as [14] 2π 4π g ; Sðλ; gÞ ¼ jdIðλ; gÞ=dgj ¼ sin λ λ S2λ ðλ1 ; λ2 ; gÞ ¼
ð3Þ
min½λ1 ; λ2 max½Sðλ1 ; gÞ; Sðλ2 ; gÞ; 2π ð4Þ
where S2λ is the sensitivity of a sensor under two wave illumination and takes on the higher sensitivity value of the two sensitivity measurements performed using λ1 and λ2 separately. λ1 and λ2 sources are considered to be adjusted to equal intensity levels; therefore, S2λ is normalized with respect to the minimum wavelength, as the lower wavelength results in higher sensitivity for a fixed intensity level. For similar wavelength sources having equal intensity, the sensitivity difference is negligible. A calibration routine involving a reference frame and two consecutive frames captured with λ1 and λ2 at a different gap are necessary to identify which wavelength result in higher sensitivity for each pixel. This calibration may also be used for correcting spatial variations of the illumination beams, which loosens the requirements of having equal intensity sources or perfect beam homogenization. Results can then be stored in a look-up-table. For the thermal sensor array used in the experiments, the gap can be varied by changing the sensor die temperature via its controller or by imaging a uniform temperature object at a near ambient temperature. Figure 1(c) illustrates the thermal imaging experimental setup,
which is described in detail at the Experimental Results Section. This part of the setup is subject to modification for other applications. Selection of λ1 and λ2 plays a critical role on the amount of measurement range and the S2λ sensitivity. The maximum unambiguous detection range for the 2 − λ system, also called the synthetic wavelength λS , is defined as [13] λS ¼
λ1 ⋅λ2 : jλ1 − λ2 j
ð5Þ
The unambiguous detection range increases from λ=4 for one laser readout to λS =4 for the 2 − λ readout. The highest overall sensitivity S2λ is achieved when g ¼ λS =8 [14,15]. Therefore, λ1 and λ2 should be selected such that λS ¼ 8g. There are more than one choice of wavelength pairs that could satisfy a specified “g”. Lower wavelengths result in higher slopes according to Eq. (3); however, they are not favorable due to the monitor detector constraints. Majority of the silicon detectors exhibit peak sensitivity at λ > 500 nm [16]. Although silicon detectors exhibit very high sensitivities at λ > 750 nm, higher wavelengths are undesirable both due to the decrease of the readout sensitivity Sðλ; gÞ and decrease of the visibility for the human eye, which makes alignment in a benchtop system more tedious. Based on availability, cost and all above constraints, we preferred to use red lasers (600 nm < λ < 700 nm) for theoretical analysis and experiments. A wide range of red laser diodes emitting at different wavelengths are available in the market (λ ¼ 635, 637, 639, 640, 642, 650, 658, 660, 670, 685, 690, 700 nm) from which illumination sources can be selected [16]. Based on Eq. (5) and available laser diode wavelengths, it is possible to achieve an optimal sensitivity gap from 1 up to 25 μm. Intermediate gap values can be addressed exploiting different wavelength combinations as well, without the need for a tunable, high cost laser light source. Laser stability and bandwidth (Δλ) are other crucial elements that determine the amount of displacement enhancement for readout using two wavelengths. Laser bandwidth determines the coherence length (λ2 =Δλ) of the interferogram that sets a limit for the maximum detectable displacement. Therefore, the coherence length of both sources should be >λS =4. Furthermore, the stability tolerance for a given detection range can be as severe as λ=1000 [17]. Battery operated, low cost laser diode control units are available in the market, which can precisely control the feed current and temperature in order to satisfy the stability tolerances. 3. Analytical Modeling
Analytical modeling is established considering the thermal imaging sensor that is used in the experiments. The model addresses readout sensitivity with respect to statistical gap variations and is adaptable 1 July 2011 / Vol. 50, No. 19 / APPLIED OPTICS
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to any type of grating based sensor array. The mean gap of thermal imaging sensor arrays operating in the 8 –14 μm long wave IR wavelength range is typically around 2:25 μm [9]. The two wavelengths considered for the readout are λ1 ¼ 650 nm and λ2 ¼ 633 nm, respectively. The sensitivity around the mean gap (g0 ), assuming the same gap value for λ1 and λ2 measurements, is calculated using Eq. (3) and can be observed in Fig. 2. At g0 ¼ 2:25 μm, the normalized sensitivity (normalization is performed with respect to the maximum sensitivity) is ∼0:5 for both wavelengths. The overall sensitivity increases with temperature change, as the arrows suggest: a decrease of gap causes an increase in the sensitivity of the λ1 readout and an increase in the gap causes an increase in the sensitivity of the λ2 readout setting a lower limit of 0.5 for the sensitivity [14,15]. For statistical analysis, the gap of each sensor within the array is modeled as random variable, such that g ¼ Nðg0 ; σÞ;
ð6Þ
where N stands for a normal distribution (Gaussian random variable). As previously mentioned, g0 ¼ 2:25 μm and three different standard deviation values were investigated: σ ¼ 10, 15, 20 nm. Two approaches are followed for calculating the sensitivity of 2000 pixels in the array that provides large enough sample space for the numerical simulations.
during λ1 and λ2 measurements are taken as independent random variables with the same statistical properties, such that g1 ¼ Nðg0 ; σÞ and g2 ¼ Nðg0 ; σÞ. (The overall sensitivity is calculated based on Eq. (4) using g1 and g2 on the right side of the equation instead of g). Figure 3 illustrates expected sensitivity histograms for λ1 and λ2 measurements based on both approaches (same and different sets of gaps for λ1 and λ2 measurements) for σ ¼ 10, 15, 20 nm. A sensitivity enhancement of 20%–40% is observed on the average sensitivity. The sensitivity enhancement with the 2 − λ readout is higher at higher σ values, where the gap variation within the sensor array is less uniform, as expected. Furthermore, the sensitivity histograms are more spread out for higher σ values. The 2 − λ readout method is beneficial where there is significant gap variation among the array elements (large σ), and it converges to the sensitivity of a single wavelength readout if the gap is constant for all array elements. The combined sensitivity histograms using the synchronous approach exhibits a minimum sensitivity limit as previously described and illustrated in Fig. 2. On the other hand, the combined histograms calculated with the asynchronous approach are smooth and spread over a wider range of sensitivity values. If there is no change between two consecutive
i. The synchronous approach assumes that the sensor gap remains constant in between λ1 and λ2 measurements. This approach is valid where sensor displacements within one frame can be neglected, or two monitoring cameras are used to capture different sources simultaneously. Therefore, the gap distribution of the sensor array for both measurements are equal such that g ¼ g1 ¼ g2 ¼ Nðg0 ; σÞ. The overall sensitivity is then calculated using Eq. (4). ii. The asynchronous approach assumes the gap changes between two measurements performed with λ1 and λ2 . For a thermal imaging sensor array [9], this approach accounts for any temperature or position change of the target between measurements. Assuming a small and independent change between measurements that slightly alters individual sensor gaps without significantly changing overall gap statistics (such as a movement or shift of the target between measurements), the gap distributions g1 and g2
Fig. 2. (Color online) Sensitivities: Sðλ1 ; gÞ and Sðλ2 ; gÞ with respect to the gap change. Any displacement around the mean gap: g0 ¼ 2:25 μm causes an increase in the combined sensitivity. 3292
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Fig. 3. (Color online) Expected sensitivity histograms with λ1 , λ2 , and combined λ1 , λ2 readout assuming the same set of gap values for the sensor array g1 ¼ g2 ¼ Nðg0 ; σÞ (synchronous), and assuming different and independent set of gap values: g1 ¼ Nðg0 ; σÞ, g2 ¼ Nðg0 ; σÞ (asynchronous), for the sensor array during λ1 , λ2 measurements for σ ¼ 10, 15, and 20 nm. “μ” denotes the average sensitivity of histograms.
frames, then the sensitivity is expected to converge to that of the synchronous case. 4. Experimental Results
Sensitivity enhancement was demonstrated using previously fabricated thermal imaging sensor arrays, which relies on a thermomechanical bending principle. The sensor operation principle is thermomechanical, i.e., the structure bends in response to the target temperature. The mechanical displacement creates an intensity change, which is monitored by observing the first diffracted order with a photodetector or a CCD camera for an array of sensors, as illustrated in Figs. 1(b) and 1(c) [9]. A 160 × 120 array of thermal imaging sensors with a 50 μm pitch were uniformly illuminated in one shot with two sources of wavelengths 633 and 650 nm, where the beams are expanded and truncated to minimize spatial variations in the beam profile [Fig. 1(b)]. Therefore, the spatial variations in the diffracted order intensities are rather attributed to the nonuniformity in the sensor gaps. Furthermore, it is worthy to note that the optical readout is not limited to sources having equal intensities. Spatial variations of the laser profiles after beam homogenization can be digitally corrected by acquiring a set of calibration images prior to data acquisition. It is best to limit this variation as it would use up the usable dynamic range. The maximum sensitivity point of th e2 − λ readout, which is at λS =8, is found to be ∼3 μm for the wavelength combination, which is sufficiently close to the mean gap g0 ¼ 2:25 μm. The sensor array
was placed in vacuum due to performance requirements, in order to eliminate thermal conduction and convection path through the air [9]. Furthermore, an IR lens was placed at the front side of the sensor array to image the target onto the array. A periodic slab cut within a printed circuit board (PCB) of size 6 × 6 cm, illustrated in Fig. 1(c) and with more detail in Fig. 4(a), was placed in front of an IR heater as a target to have a clear distinction between hot and cold areas. Note that it is necessary to monitor the diffracted order intensity at two different but sufficiently close gap and intensity values in order to approximate the sensitivity term given in Eq. (3). For a thermomechanical sensor, the change in the gap is linearly proportional with the applied temperature [9]. Therefore, the sensitivity was found based on the intensity change of the sensors with respect to two different heater temperatures: T 1 (heater on) and T 2 (heater off), where T 1 − T 2 ¼ 250 °C. In the experimental setup, the data was monitored in realtime with the CCD camera, and saved. Once the procedure was repeated for the second wavelength, the data can be processed within a few seconds using MATLAB computing software. Figure 4(b) illustrates a zoomed image of the captured first order diffracted light of ∼50 sensors. Differential images were calculated for the entire array for both wavelengths, which are illustrated in Figs. 4(c) and 4(d), by subtracting images taken during the on and off states of the heater for two laser sources, in the configuration shown in Figs. 1(b) and 1(c). The sensitivity histograms shown in Figs. 4(f)
Fig. 4. (Color online) (a) Target used in the experiment: periodic PCB slab, which is placed in front of an IR heater. (b) Zoomed image of about 50 sensors captured by using first order diffracted light. (c) Image of 20, 000 sensors by using first order diffracted light acquired by λ1 . (e) Same image acquired by λ2. (e) Combined image of (c) and (d) using a postdetection signal processing by taking the larger change with respect to the reference image. (f) Histogram of the λ1 difference image. (g) Histogram of λ2 difference image. (h) Histogram of the combined image. The average sensitivity μ increases from 17 CCD levels for each individual image up to 22.7 CCD levels. 1 July 2011 / Vol. 50, No. 19 / APPLIED OPTICS
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Table 1.
Comparison of Synchronous and Asynchronous Modes of Operation in Two-Wavelength Readouta
Readout Approach Sensor gap Readout camera Optical components for wavelength switching
Synchronous Operation
Asynchronous Operation
g1 ¼ g2 2 detector arrays or CCD cameras • Polarizing beam splitter
g1 ≠ g2 1 detector array or a CCD camerab
• Narrowband color filters
• Pulsing the lasers time-sequentially • Ferroelectric liquid crystals polarization rotator and a polarizer to transmit one laser at a time • Rotating narrowband coated color filters to transmit one laser at a time
a b
A variety of optical hardware components are listed for both modes for wavelength separation. The asynchronous mode converges to the synchronous case for slowly varying signals.
and 4(g) are displayed based on the absolute intensity changes of the areas shown with white rectangles, which correspond to the openings in the periodic slab, where ∼2000 among 20, 000 sensors are illuminated. Finally the combined image [Fig. 4(e)] and histogram [Fig. 4(h)] are calculated based on Eq. (4), where the CCD level changes correspond to dIðλ; gÞ= dg for small CCD level changes observed during the experiment (
